cs583, bing liu, uic 1 clustering clustering is a technique for finding similarity groups in data,...

CS583, Bing Liu, UIC 1

Clustering Clustering is a technique for finding similarity groups

in data, called clusters. I.e., it groups data instances that are similar to (near) each other

in one cluster and data instances that are very different (far away) from each other into different clusters.

Clustering is often called an unsupervised learning task as no class values denoting an a priori grouping of the data instances are given, which is the case in supervised learning.

Due to historical reasons, clustering is often considered synonymous with unsupervised learning. In fact, association rule mining is also unsupervised

This chapter focuses on clustering.


Aspects of clustering A clustering algorithm

Partitional clustering Hierarchical clustering …

A distance (similarity, or dissimilarity) function Clustering quality

Inter-clusters distance maximized Intra-clusters distance minimized

The quality of a clustering result depends on the algorithm, the distance function, and the application.


K-means clustering K-means is a partitional clustering algorithm Let the set of data points (or instances) D be

{x1, x2, …, xn},

where xi = (xi1, xi2, …, xir) is a vector in a real-valued space X Rr, and r is the number of attributes (dimensions) in the data.

The k-means algorithm partitions the given data into k clusters. Each cluster has a cluster center, called centroid. k is specified by the user


K-means algorithm

Given k, the k-means algorithm works as follows: 1) Randomly choose k data points (seeds) to be the

initial centroids, cluster centers

2) Assign each data point to the closest centroid

3) Re-compute the centroids using the current cluster memberships.

4) If a convergence criterion is not met, go to 2).


K-means algorithm – (cont …)


Stopping/convergence criterion 1. no (or minimum) re-assignments of data

points to different clusters, 2. no (or minimum) change of centroids, or 3. minimum decrease in the sum of squared

error (SSE),

Ci is the jth cluster, mj is the centroid of cluster Cj (the mean vector of all the data points in Cj), and dist(x, mj) is the distance between data point x and centroid mj.

k

jC jj

distSSE1

2),(x

mx (1)


An example

++


An example (cont …)


An example distance function


Strengths of k-means Strengths:

Simple: easy to understand and to implement Efficient: Time complexity: O(tkn),

where n is the number of data points,

k is the number of clusters, and

t is the number of iterations. Since both k and t are small. k-means is considered a

linear algorithm. K-means is the most popular clustering algorithm. Note that: it terminates at a local optimum if SSE is

used. The global optimum is hard to find due to complexity.


Weaknesses of k-means

The algorithm is only applicable if the mean is defined. For categorical data, k-mode - the centroid is

represented by most frequent values. The user needs to specify k. The algorithm is sensitive to outliers

Outliers are data points that are very far away from other data points.

Outliers could be errors in the data recording or some special data points with very different values.


Weaknesses of k-means: Problems with outliers


Weaknesses of k-means: To deal with outliers One method is to remove some data points in the

clustering process that are much further away from the centroids than other data points. To be safe, we may want to monitor these possible outliers

over a few iterations and then decide to remove them. Another method is to perform random sampling.

Since in sampling we only choose a small subset of the data points, the chance of selecting an outlier is very small. Assign the rest of the data points to the clusters by

distance or similarity comparison, or classification


Weaknesses of k-means (cont …) The algorithm is sensitive to initial seeds.


Weaknesses of k-means (cont …) If we use different seeds: good results

There are some methods to help choose good seeds


Weaknesses of k-means (cont …) The k-means algorithm is not suitable for

discovering clusters that are not hyper-ellipsoids (or hyper-spheres).

+


K-means summary Despite weaknesses, k-means is still the

most popular algorithm due to its simplicity, efficiency and other clustering algorithms have their own lists of

weaknesses. No clear evidence that any other clustering

algorithm performs better in general although they may be more suitable for some

specific types of data or applications. Comparing different clustering algorithms is a

difficult task. No one knows the correct clusters!

cs583, bing liu, uic 1 clustering clustering is a technique for finding similarity groups in data,...

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